Estimating Knee Movement Patterns of Recreational Runners Across Training Sessions Using Multilevel Functional Regression Models

Modern wearable monitors and laboratory equipment allow the recording of high-frequency data that can be used to quantify human movement. However, currently, data analysis approaches in these domains remain limited. This article proposes a new framework to analyze biomechanical patterns in sport training data recorded across multiple training sessions using multilevel functional models. We apply the methods to subsecond-level data of knee location trajectories collected in 19 recreational runners during a medium-intensity continuous run (MICR) and a high-intensity interval training (HIIT) session, with multiple steps recorded in each participant-session. We estimate functional intra-class correlation coefficient to evaluate the reliability of recorded measurements across multiple sessions of the same training type. Furthermore, we obtained a vectorial representation of the three hierarchical levels of the data and visualize them in a low-dimensional space. Finally, we quantified the differences between genders and between two training types using functional multilevel regression models that incorporate covariate information. We provide an overview of the relevant methods and make both data and the R code for all analyses freely available online on GitHub. Thus, this work can serve as a helpful reference for practitioners and guide for a broader audience of researchers interested in modeling repeated functional measures at different resolution levels in the context of biomechanics and sports science applications.

现代可穿戴监测设备与实验室仪器可采集高频数据，用于量化人体运动状态。然而当前该领域的数据分析方法仍存在局限。本文提出一种基于多层泛函模型（multilevel functional models）的新框架，用于分析多训练场次采集的运动训练数据中的生物力学模式。我们将该方法应用于19名休闲跑者的亚秒级（subsecond-level）膝关节位置轨迹（knee location trajectories）数据：受试者分别完成中等强度持续跑（Medium-Intensity Continuous Run, MICR）与高强度间歇训练（High-Intensity Interval Training, HIIT），且每个训练场次中采集了多步运动数据。我们通过泛函组内相关系数（functional intra-class correlation coefficient）评估同一训练类型下多场次采集数据的可靠性。此外，我们对数据的三个层级结构进行向量化表征，并在低维空间中完成可视化。最后，我们通过纳入协变量信息的泛函多层回归模型（functional multilevel regression models），量化了性别间与两种训练类型间的运动模式差异。本文梳理了相关方法的研究进展，并将全部分析所需的数据集与R代码（R code）开源至GitHub平台。因此，本研究可为生物力学与运动科学领域的从业者提供参考，也可为关注不同分辨率层级下重复泛函测量建模的广大研究人员提供研究思路。